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current location:Mathematical operation > History of Inequality Computation > Answer
    Overview: 1 questions will be solved this time.Among them
           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality 1 <= sqrt(x^2+(2*x-3)^2) <= 3 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities:
        1 <= sqrt ( x ^ 2 + ( 2 * x - 3 ) ^ 2 )         (1)
         sqrt ( x ^ 2 + ( 2 * x - 3 ) ^ 2 ) <= 3         (2)
        From the definition field of √
         x ^ 2 + ( 2 * x - 3 ) ^ 2 ≥ 0        (3 )

    From inequality(1):
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
    From inequality(2):
         0 ≤ x ≤ 12/5
    From inequality(3):
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!

    From inequalities (1) and (2)
         0 ≤ x ≤ 12/5    (4)
    From inequalities (3) and (4)
         0 ≤ x ≤ 12/5    (5)

    The final solution set is :

         0 ≤ x ≤ 12/5




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